It is currently 21 Oct 2017, 05:42

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A citrus fruit grower receives $15 for each crate of oranges  post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 41891 Kudos [?]: 129094 [0], given: 12194 Re: Gmat prep2 [#permalink] Show Tags 21 Apr 2012, 10:45 catty2004 wrote: Bunuel wrote: Joanna bought only$0.15 stamps and $0.29 stamps. How many$0.15 stamps did she buy?

Let $$x$$ be the # of $0.15 stamps and $$y$$ the # of$0.29 stamps. Note that $$x$$ and $$y$$ must be an integers. Q: $$x=?$$

(1) She bought $4.40 worth of stamps --> $$15x+29y=440$$. Only one integer combination of $$x$$ and $$y$$ is possible to satisfy $$15x+29y=440$$: $$x=10$$ and $$y=10$$. Sufficient. (2) She bought an equal number of$0.15 stamps and $0.29 stamps --> $$x=y$$. Not sufficient. Answer: A. So when we have equation of a type $$ax+by=c$$ and we know that x and y are integers, there can be multiple solutions possible for x and y (eg $$5x+6y=12900$$) OR just one combination (eg $$15x+29y=440$$). Hence in some cases $$ax+by=c$$ is NOT sufficient and in some cases it's sufficient. Hope it helps. How can one identify one or multiple solution for $$ax+by=c$$? (i.e. how did you arrive at the conclusion that only one integer combo satisfy $$15x+29y=440$$? Trial and error plus some logic and knowledge of basics of number properties should help you to identify this. For more on this type of questions check: eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html Hope it helps. _________________ Kudos [?]: 129094 [0], given: 12194 Manager Joined: 09 Apr 2012 Posts: 63 Kudos [?]: 67 [0], given: 29 Re: A citrus fruit grower receives$15 for each crate of oranges [#permalink]

Show Tags

12 Oct 2012, 21:20
Mixing trial and error with number properties would save you some time.

(In relation to the question with 0.15 and 0.29 stamps).

The option says 0.15x+0.29y=4.40.

15x+29y=440; 15x=440-29y...
so y has to be a multiple of 5.

at most y can be 5 or 10.(y=15 or greater would yield a negative number)
y=5 doesnot give you a solution. y=10 is the only solution. From this X can be calculated.
SUFFICIENT

11x +28y=440 Sufficient.
11x+20y=440 Sufficient.
11x +18y Not sufficient. (11x=440-18y. assuming y=11z, x=40-18z. so x could be 22 or 4).

Kudos [?]: 67 [0], given: 29